Crystal Lattice Structures
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Introduction

Simple Cubic

Body Centered Cubic

Face Centered Cubic

Primitive FCC

Simple Hexagonal

Hexagonal Closest Packing

HCP Coordination

Cubic Closest Packing

CCP Coordination

Rhombohedral

2- & 3-Layer repeats

4-layer repeats

Tetrahedral Holes

Octahedral Holes

CsCl

NaCl

Halite

Fluorite

Zinc Blende

Exercises
The Rhombohedral Lattice
  In order for the (ABC) layered lattice to be closest packed, the interlayer spacing must be exactly equal to CPIS.r with c:a = 1.5.CPIS.  Thus, the standard reduced  cell is then the special rhombohedron found in the face centered cubic lattice. 

If the c:a ratio differs from the closest packed value, then the standard reduced unit cell is still a rhombohedron (a = b = c  and a = b = g), but the cell edges need not be of length 2r and/or the inter edge angles need not be 60o. In these quasi-closest packed structures, either the hexagonal
(Z = 3) cell or the primitive (Z = 1) unit cell may be used to describe this lattice, which is called, by convention, rhombohedral. 

Note that quasi-closest packed (AB) lattices are also possible if c:a differs from CPIS.
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Steven F. Watkins, Department of Chemistry, Louisiana State University